Continuous quotients for lattice actions on compact manifolds
Dynamical Systems
2007-05-23 v1
Abstract
Let G be a subgroup of finite index in SL(n,Z) for N > 4. Suppose G acts continuously on a manifold M, with fundamental group Z^n, preserving a measure that is positive on open sets. Further assume that the induced G action on H^1(M) is non-trivial. We show there exists a finite index subgroup G' of G and a G' equivariant continuous map from M to the n-torus that induces an isomorphism on fundamental groups. We prove more general results providing continuous quotients in cases where the fundamental group of M surjects onto a finitely generated torsion free nilpotent group. We also give some new examples of manifolds with G actions to which the theorems apply.
Cite
@article{arxiv.math/0405273,
title = {Continuous quotients for lattice actions on compact manifolds},
author = {David Fisher and Kevin Whyte},
journal= {arXiv preprint arXiv:math/0405273},
year = {2007}
}